The Super BMS Algebra, Scattering and Holography

TL;DR

This paper proposes a new framework for gravitational scattering based on the super-BMS algebra, suggesting it could resolve infrared divergences and connect holography with scattering theory in flat and AdS spacetimes.

Contribution

It introduces a representation-theoretic approach to gravitational scattering using super-BMS algebra, linking holography, IR divergence resolution, and spacetime symmetries.

Findings

Representation spaces generalize massless particle Fock space

Scattering amplitudes may be IR divergence free

Holographic Space-Time formalism regulates singularities

Abstract

I propose that the proper framework for gravitational scattering theory is the rep- resentation theory of the super-BMS algebra of Awada, Gibbons and Shaw[1], and its generalizations. Certain representation spaces of these algebras generalize the Fock space of massless particles. The algebra is realized in terms of operator valued measures on the momentum space dual to null infinity, and particles correspond to smearing these measures with delta functions. I conjecture that scattering amplitudes defined in terms of characteristic measures on finite spherical caps, the analog of Sterman-Weinberg jets[2], will have no infrared (IR) divergences. An important role is played by singular functions concentrated at zero momentum, and I argue that the formalism of Holographic Space- Time is the appropriate regulator for the singularities. It involves a choice of a time-like trajectory in Minkowski space. The condition that physics be independent of this choice of trajectory is a strong constraint on the scattering matrix. Poincare invariance of S is a particular consequence of this constraint. I briefly sketch the modifications of the formalism, which are necessary for dealing with massive particles. I also sketch how it should generalize to AdS space-time, and in particular show that the fuzzy spinor cutoff of HST implements the UV/IR correspondence of AdS/CFT.